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# A a lh x0 h ax x a 1 x ax0 x0 max 0x 2

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Unformatted text preview: ורפי ל 2‪l‬‬ ‫3. יהי ‪ H‬מרחב הילברט ו־ ‪ E1 , E2 ⊆ H‬תתי מרחבים סגורים. הראו ש‬ ‫⊥‬ ‫⊥‬ ‫2 ‪( E 1 ∩ E 2 ) ⊥ = E1 + E‬‬ ‫⊥‬ ‫⊥‬ ‫, 2 ‪( E 1 + E 2 ) ⊥ = E1 ∩ E‬‬ ‫האם התנאי ש 2‪ E1 , E‬סגורים הכרחי?‬ ‫4. יהי ‪ H‬מרחב הילברט, הראו שאם ) ‪ A ∈ L(H‬צמוד לעצמו אז )‪i ∈ σ (A‬‬ ‫/‬ ‫5. האם המערכת הבאה שלמה ב 2‪l‬‬ ‫)... ,0 ,0 ,1− ,‪x1 = (1, −1, 0, 0, ...), x2 = (0, 1, −1, 0,...
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